Counting Summations

Problem Statement

It is possible to write five as a sum in exactly six different ways:

$$\begin{align} &4 + 1\\ &3 + 2\\ &3 + 1 + 1\\ &2 + 2 + 1\\ &2 + 1 + 1 + 1\\ &1 + 1 + 1 + 1 + 1 \end{align}$$

How many different ways can $2^N$ be written as a sum of at least two positive integers? Give your answer modulo $1000000007$.

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You need to submit in the format: "N:problem(N)", possibly with multiple values at once, separated by commas, with $N$ between $1$ and $100$.

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